This paper concerns the existence and multiplicity of solutions for the Schrődinger–Kirchhoff
type problems involving the fractional p–Laplacian and critical exponent. As a particular …

In this paper we study the existence and concentration behaviors of positive solutions to the
Kirchhoff type equations-ε^ 2 M\left (ε^ 2-N\!\! R^ N| ∇ u|^ 2\, dx\right) Δ u\!+\! V (x) u\!=\! f …

In this paper, we study the following nonlinear Maxwell–Dirac system α·(i ħ∇+ q (x) A (x)) ua
β u+ V (x) uq (x) ϕ (x) u=| u| p-2 u,-Δ ϕ= q (x)| u| 2,-Δ A k= q (x)(α ku)· u, k= 1, 2, 3, for x∈ R 3 …

We are concerned with the study of two classes of nonlinear problems driven by differential
operators with unbalanced growth, which generalize the (p, q)-and (p (x), q (x))-Laplace …

We deal with a class on nonlinear Schrödinger equations (NLS) with potentials V (x)∼| x|−
α, 0< α< 2, and K (x)∼| x|− β, β> 0. Working in weighted Sobolev spaces, the existence of …

We consider two-dimensional Bose–Einstein condensates with attractive interaction,
described by the Gross–Pitaevskii functional. Minimizers of this functional exist only if the …

We study the nonlocal equation-ε^ 2 Δ u_ ε+ V u_ ε= ε^-α\bigl (I_ α*| u_ ε|^ p\bigr)| u_ ε|^ p-2
u_ ε\quad in R^ N,-ε 2 Δ u ε+ V u ε= ε-α (I α∗| u ε| p)| u ε| p-2 u ε in RN, where N ≥ 1 N≥ 1, α …

This introduction to the singularly perturbed methods in the nonlinear elliptic partial
differential equations emphasises the existence and local uniqueness of solutions exhibiting …

For elliptic equations of the form Δu-V(εx)u+f(u)=0,x∈\bfR^N, where the potential V satisfies
|x|→∞V(x)>\bfR^NV(x)=0, we develop a new variational approach to construct localized …

For elliptic equations ε 2 Δ u− V (x) u+ f (u)= 0, x∈ RN, N≧ 3, we develop a new variational
approach to construct localized positive solutions which concentrate at an isolated …